WildCattle, "pyroxylee"--unlike "nitro" in some other countries--was not an officially required stamp of the French proofhouses. Therefore, there really isn't any "official" French term for smokeless. It's similar to "arquebusier" and "armurier"--both of which you will find on French guns, thus neither being the "official" term for gunmaker, since neither was a proofhouse marking. French for smokeless proof, as far as the proofhouses were concerned: either star or crown over PT. (And the P stands for poudre, not pyroxylee. On that issue, if you wish, I could quote you General Journee.)
Rabbit and JC, whether 3 crowns meant double proof or triple proof depends on when the gun underwent proof. According to Kennett (agree with Ted that his article is excellent), it originally meant double proof at 20,500 psi. It's now (since 1924) called triple proof . . . but the pressure reduced to 18,000 psi (still darned stout!) The previous superior (two crowns) is now called double--which makes sense, given the number of crowns. But leave it to the French to try to confuse us!